Tagg Romney, son of 2012 Republican presidential nominee Mitt Romney, said today he would not run for the Massachusetts US Senate seat opening up because of the departure of John F. Kerry to be secretary of state.

Former governor William F. Weld and former lieutenant governor Kerry Healey also said they would not run, leaving few strong options for Bay State Republicans hoping for a victory in the June 25 special election in the traditionally blue state.

“I love my home state and admit it would be an honor to represent the citizens of our great Commonwealth. However, I am currently committed to my business and to spending as much time as I can with my wife and children,” Romney said this afternoon in an e-mailed statement, while noting that he was humbled by the “outreach” he had received over the weekend encouraging him to run.

Weld issued a one-sentence statement this morning, saying that he would not run.

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“While I am grateful for the kind expressions of support and encouragement which I have received, I will not be a candidate for United States Senator from Massachusetts in the special election this year,’’ Weld said in the statement released by his law firm.

The announcement by Weld did not surprise Weld’s law partner at the law firm, Mintz Levin, and affiliate ML Strategies.

In a brief telephone interview, Stephen Tocco said Weld has focused on building his law practice since joining the firm. Weld also has been traveling extensively for his clients, including recent trips to Africa and Canada.

“He seems to be settling in quite well,’’ said Tocco, who added that Weld seemed content with his current job. “He’s been a great addition to the firm.’’

Republicans have been scrambling to find a strong candidate former US Senator Scott Brown’s decision last week not to run. The telegenic Brown had won the state’s other Senate seat in a stunning surprise victory in a 2010 special election but then lost it to Elizabeth Warren last year. Brown said he wasn’t sure that returning to a partisan Senate was the best way for him to continue in public service and said he knew it was “not the only way for me to advance the ideals and causes” that mattered to him.

Other big-name Republicans who have already passed on a Senate run include Charles D. Baker, who ran for governor in 2010, and Richard R. Tisei, who ran for lieutenant governor with him.

Meanwhile, on the Democratic side of the race there was another abstention today — this one from Middlesex District Attorney Gerard T. Leone.

Veteran US Representatives Edward J. Markey and Stephen F. Lynch are battling for the Democratic nomination.

Leone had been seen as a potentially strong candidate, too, for the Democratic nod. But he said this afternoon in a statement that he remained set on leaving “electoral politics and government service to pursue other career opportunities.”

The Senate is a “wonderful public service opportunity to do significant and gratifying things for people,” he said, but “it is not the right next step for me by way of the job or the lifestyle. These are highly personal decisions, that are never wrong nor regrettable when made in the best interest of family.”

One man who said today that he is running is Jack E. Robinson, who has run a number of long-shot, unsuccessful races for major offices, including a 2000 Republican run against the late senator Edward M. Kennedy and a 2009 GOP primary race against Scott Brown. He announced today that he had pulled nomination papers from the secretary of state’s office and would run this time as an independent.

Robinson said he was running as an independent because “extremism from both parties is preventing the 21st century from being the new American century. As an independent, I can bridge the gap in Washington and be a voice of the people and not of a party.”

Robinson must file 10,000 signatures with local city and town clerks by April 3 and then bring the certified signatures to the secretary of state’s office by April 16 in order to win a spot as an independent candidate on the June 25 ballot, said Brian McNiff, spokesman for Secretary of State William F. Galvin.

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